2026/07/27 by Kanoa Pick, Falk Feddersen
paper · doi:10.1017/jfm.2026.11869
The shape of depth-limited overturning waves strongly influences turbulence and sediment transport in the surf zone. Bathymetric slope s s s and initial wave height upper H 0 divided by h 0 H 0 / h 0 H0/h0 are key parameters that govern wave overturning shape, yet their effect has not been quantified. We use a two-dimensional fully nonlinear potential flow model to study shoaling and overturning solitary waves across a range of s s s and upper H 0 divided by h 0 H 0 / h 0 H0/h0 representing spilling and plunging waves. Near-constant domain volume and energy demonstrate the model’s accuracy. Gentler slopes yield smaller, more inclined overturns with thinner jets, whereas steeper slopes produce larger, more horizontally inclined overturns with thicker jets. Wave breaking and overturning parameters such as breaker depth index, overturn area, jet area, aspect ratio and overturn angle are examined. Non-dimensional overturn and jet areas increase with steeper slopes and smaller upper H 0 divided by h 0 H 0 / h 0 H0/h0 . Aspect ratios increase similarly but more slowly, while overturn angles shift from inclined to horizontal. A scaling parameter s divided by left parenthesis upper H 0 divided by h 0 right parenthesis Superscript 1 divided by 4 s / ( H 0 / h 0 ) 1 / 4 s/(H0/h0)1/4 scales these wave breaking and overturning parameters well. During shoaling, front-face wave steepening occurs more rapidly for larger slopes and smaller upper H 0 divided by h 0 H 0 / h 0 H0/h0 . Wave overturn shape is linked to wave steepening rate, which also scales with slope and upper H 0 divided by h 0 H 0 / h 0 H0/h0 . Empirical expressions for overturning parameters and wave steepening rate are found. The jet potential energy, related to the wave dissipation at jet impact, is a strong function of jet area, linking overturning wave shape to the turbulence that drives sediment suspension and transport.